Systems of Differential Equations · Easy problem

The matrix $A=\begin{pmatrix}1&-1\\1&3\end{pmatrix}$ has a repeated eigenvalue $\lambda$ with eigenvector $\mathbf v=\begin{pmatrix}1\\-1\end{pmatrix}$. A generalized eigenvector $\mathbf w$ satisfies $(A-\lambda I)\mathbf w=\mathbf v$; one such vector has the form $\mathbf w=\begin{pmatrix}0\\k\end{pmatrix}$. Find $k$.